The invention relates to a method and apparatus for controlling the position of a rotating element of a machine tool.
For example, in the production of helical gearings on workpieces by hob peeling, the axes of the workpiece and of the tool cross each other and the workpiece and the tool rotate about their axes. The tool or the workpiece is moved at a feed rate parallel to the workpiece axis. During this process, the workpiece or the tool is given a corresponding additional rotation for generating the pitch of the helix.
In the hob peeling described the tool is joined to a main guide element, the spindle, and the workpiece is joined to a reference element, the workpiece spindle. The movement of the tool to be carried out during machining is composed of two relative movements consisting of a continuous indexing movement and a helical movement. The indexing movement consists of the tool and the workpiece rotating at rates which are inverse ratios of their numbers of teeth. The helical movement is produced by the tool or the workpiece being shifted in the direction of the workpiece axis and the workpiece executing an additional rotation relative to the tool. The following relation holds good for this helical movement when using a spur-toothed tool: ##EQU1## Here .DELTA..zeta. is the additional angle of rotation referred to the workpiece spindle of a cutting machine, .DELTA.z is the displacement of the tool or of the workpiece in the direction of the workpiece axis, .beta. is the helix angle of the toothing of the workpiece and r is the pitch circle radius of the workpiece toothing. Considering the conditions after one rotation of the workpiece in each case, for example, a .DELTA..zeta.=0.0024 is obtained for .DELTA.z=0.2 mm, .beta.=20.degree., r=30 mm. This results in .beta..zeta./2.pi.=0.00039, which means that in this example the basic rotation is approximately 2,560 times faster than the additional rotation. In general, as also in this example, the additional movement is slow compared with the basic movement.
If the movements are implemented via mechanical gear trains in the cutting machine, the deviations in transmission of the gear trains are significant in determining the machine characteristics. Thus, a measurement is required. If, in contrast, the movements are to be generated via individual drive mechanisms in combination with electronics, the measurement is a prerequisite for the movements to be produceable at all.
Normally, these measurements are based on the principle that a moving part is selected as a reference element and the instantaneous nominal position of this reference element is calculated from the instantaneous position of the remaining parts, taking into account the deviation-free transmission ratios to the reference element. The calculated nominal position is compared with the actual value. The result of this comparison is the measurement value. It can be used for correcting the instantaneous position of the guided part.
In the case of hob peeling, during each revolution of the workpiece, the tool machines a narrow strip of the flanks of the toothing to be produced. As a result of the superimposed helical movement, the narrow strip is threaded along the basic workpiece body and thus the toothing is produced over the entire width of the tooth trace. Accordingly, the helical movement produces the toothed face on the workpiece. Disregarding tooth trace modifications in which the tooth traces are intended not to be exactly helical lines, in order to improve the running characteristics of the finished toothed wheels in the gear mechanism, the ideal tooth trace of a cylindrical gear is a helical line.
To be able to produce this helical line as accurately as possible, the resolution of the measurement values used for determining the additional rotation for generating the helical line must not be too coarse. If the resolution of the measurement value for detecting the additional rotation is too coarse, the desired helical line is approximated by a stepped space curve during the measurement or during the controlling process. In the case of machines for machining workpieces having a diameter of, for example, 200 mm, a resolution of 0.5 /.mu.m is desirable. This would mean that a pulse transmitter on the workpiece spindle of the cutting machine, if necessary followed by an interpolator, would have to supply approximately 600,000 pulses per spindle rotation. Although such pulse transmitters are known, they can only be used at a low number of revolutions or speed. The highest permissible number of revolutions of such pulse transmitters is at present about 50 to 100/min. But the spindles of the cutting machine should be able to operate at numbers of revolutions above 1,000/min. This excludes the methods using pulse scales, used at present for measuring the position of elements moving relative to each other.
It has already been mentioned that the tooth traces of cylindrical gears should in some cases not be exactly helical lines, in order to improve their running characteristics in the gear mechanism. It is possible to produce such gears by hob peeling by producing, for example, the right-hand and left-hand flanks in separate work cycles. During this process, the above-mentioned additional rotation is not proportional to the displacement of the tool or of the workpiece in the direction of the workpiece axis but the desired tooth-trace modification is superimposed on this additional rotation as a function of the axial slide position.